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arXiv:0911.3030

Quantum entanglement in soliton fractionalisation process

S. Arunagiri

Published Nov 16, 2009• 0 citations
arXivHTMLPDF

Abstract

Quantum state, in relativistic quantum mechanics, itself turns out to be an entangled state due to its own degrees freedom such as spin and momentum. This peculiar entanglement leaves the transformed state mixed. We consider the fractional charge state that arises in a theory of fermion interacting with scalar background in this context. The apparent entanglement occurs between fermion ans scalar through Yukawa-type interaction. However, the spontaneous symmetry breaking causes appearance of the $c$-number zero energy solution of the Dirac equation as a pure state. Quantum entanglement in such relativistic system is proposed to have a microscopic view of the spontaneous symmetry breaking which has been realised in condensed matter system like polyacetylene.

DOI
10.48550/arxiv.0911.3030

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Abstract In this paper we study the single particle entanglement induced by a Lorentz boost. We described the particle as a solution of the free Dirac equation, a Dirac bispinor, and compare the induced momentum-spin entanglement with the result obtained in the widely considered framework of relativistic spin 1/2 states. The spin linear entropy for both approaches agree in the ultra relativistic limit. We also verify that the spin-momentum entanglement differers from the spin entropy for the bispinorial case, indicating a true multipartite entanglement involving the degrees of freedom of a Dirac bispinor state: momentum, spin and intrinsic parity. The fact that Dirac bispinors belongs to an irreducible representation of the complete Lorentz group, which also included parity as a symmetry, is the ultimate reason behind such non-trivial structure.
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I present some general ideas about quantum entanglement in relativistic quantum field theory, especially entanglement in the physical vacuum. Here, entanglement is defined between different single particle states (or modes), parametrized either by energy-momentum together with internal degrees of freedom, or by spacetime coordinate together with the component index in the case of a vector or spinor field. In this approach, the notion of entanglement between different spacetime points can be established. Some entanglement properties are obtained as constraints from symmetries, e.g., under Lorentz transformation, space inversion, time reverse, and charge conjugation.
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Analysis of the generation of spin entanglement from nonrelativistic QED is presented. The results of entanglement are obtained with relativistic correction to the leading order of (v/c)2.{(v/c)}^{2}.(v/c)2. It is shown that to this order, the degree of entanglement of a singlet state does not change under time evolution, whereas the triplet state can change.